It is already known, for example from Swedish Patents 9602554-9 (506850) and 9602555-6 (506849), to provide such a tooth prosthesis system by means of which implantation and tooth prosthesis structuring can be executed in a very short time compared with the current times of 3 to 6 months. Reference is also made to the BR{dot over (A)}NEMARK NOVUM® system which is described for example in “Clinical Implant Dentistry and Related Research, Volume 1, Number 1, 1999” and the publication “Br{dot over (a)}nemark Osseointegration Center, May 99”. The concept is also described in the “Manual for Clinical Investigation 1999”. From the first-mentioned patent specification it is known to use a superstructure which expediently comprises a separate rail with securing members and a tooth prosthesis bridge which can be attached to the rail (see, for example, page 5, paragraph 4). The use of two matching upper and lower parts which are intended to bear against each other via a contact surface is also shown in detail in said “Manual”.